Hazard will double his wages to £400,000 in a five-year deal at Madrid, becoming the club's second major signing of the summer after Frankfurt striker Luka Jovic. His arrival takes Madrid's spending to around 300 million euros (340 million USA dollars) ahead of next season.
He joined Chelsea in 2012, scoring 85 goals in over 200 games since.
"I can't be compared to (Lionel) Messi", Hazard, who was directly involved in more Premier League goals than anyone else this term, responded.
Hazard's arrival in the Spanish capital makes him Real Madrid's fourth signing of the summer transfer window already.
"Leaving Chelsea is the biggest and toughest decision in my career to date", Hazard wrote on his official Facebook page.
"The memories he leaves us with will not fade".
Real Madrid finished third in La Liga last season and failed to reach the finals of the Champions League and Copa del Rey. This season also saw the Belgian winning the PFA Fans' Player of the Year and the Premier League Playmaker of the Year award for his 31 goal contributions in 37 appearances in the English top-flight.
Eden Hazard who is a Belgian Professional footballer, will be now known as a former player of Chelsea Football club.
"Eden and I have known each other since we are young boys", Benteke said.
With that in mind, Hazard is expected to play off the left flank, where his supreme ability with both feet can really shine.
Belgium now face Scotland at home on Tuesday in the next instalment of their Euro 2020 campaign with Hazard set to travel to Madrid the following day ahead of the Santiago Bernabéu presentation on Thursday.
The French-speaking Real stopper told Hazard in Spanish: "Welcome to the best club in the world".